Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ atan(sin(x)/(2*(1+cos(x))))/2

¿Cómo vas a descomponer esta atan(sin(x)/(2*(1+cos(x))))/2 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    /    sin(x)    \
atan|--------------|
    \2*(1 + cos(x))/
--------------------
         2
atan⁡(sin⁡(x)2(cos⁡(x)+1))2\frac{\operatorname{atan}{\left(\frac{\sin{\left(x \right)}}{2 \left(\cos{\left(x \right)} + 1\right)} \right)}}{2} 
atan(sin(x)/((2*(1 + cos(x)))))/2
Descomposición de una fracción [src] 
atan(sin(x)/(2 + 2*cos(x)))/2
atan⁡(sin⁡(x)2cos⁡(x)+2)2\frac{\operatorname{atan}{\left(\frac{\sin{\left(x \right)}}{2 \cos{\left(x \right)} + 2} \right)}}{2} 
    /   sin(x)   \
atan|------------|
    \2 + 2*cos(x)/
------------------
        2
Potencias [src] 
    /   sin(x)   \
atan|------------|
    \2 + 2*cos(x)/
------------------
        2
atan⁡(sin⁡(x)2cos⁡(x)+2)2\frac{\operatorname{atan}{\left(\frac{\sin{\left(x \right)}}{2 \cos{\left(x \right)} + 2} \right)}}{2} 
     /   /   -I*x    I*x\ \ 
     | I*\- e     + e   / | 
-atan|--------------------| 
     |  /     I*x    -I*x\| 
     \2*\2 + e    + e    // 
----------------------------
             2
−atan⁡(i(eix−e−ix)2(eix+2+e−ix))2- \frac{\operatorname{atan}{\left(\frac{i \left(e^{i x} - e^{- i x}\right)}{2 \left(e^{i x} + 2 + e^{- i x}\right)} \right)}}{2} 
-atan(i*(-exp(-i*x) + exp(i*x))/(2*(2 + exp(i*x) + exp(-i*x))))/2
Combinatoria [src] 
    /   sin(x)   \
atan|------------|
    \2 + 2*cos(x)/
------------------
        2
atan⁡(sin⁡(x)2cos⁡(x)+2)2\frac{\operatorname{atan}{\left(\frac{\sin{\left(x \right)}}{2 \cos{\left(x \right)} + 2} \right)}}{2} 
atan(sin(x)/(2 + 2*cos(x)))/2
Unión de expresiones racionales [src] 
    /   sin(x)   \
atan|------------|
    \2 + 2*cos(x)/
------------------
        2
atan⁡(sin⁡(x)2cos⁡(x)+2)2\frac{\operatorname{atan}{\left(\frac{\sin{\left(x \right)}}{2 \cos{\left(x \right)} + 2} \right)}}{2} 
atan(sin(x)/(2 + 2*cos(x)))/2
Abrimos la expresión [src] 
    /   sin(x)   \
atan|------------|
    \2 + 2*cos(x)/
------------------
        2
atan⁡(sin⁡(x)2cos⁡(x)+2)2\frac{\operatorname{atan}{\left(\frac{\sin{\left(x \right)}}{2 \cos{\left(x \right)} + 2} \right)}}{2} 
atan(sin(x)/(2 + 2*cos(x)))/2
Respuesta numérica [src] 
0.5*atan(sin(x)/((2*(1 + cos(x)))))
0.5*atan(sin(x)/((2*(1 + cos(x)))))
Parte trigonométrica [src] 
    /                /x\            \
    |             tan|-|            |
    |                \2/            |
atan|-------------------------------|
    |              /           2/x\\|
    |              |    1 - tan |-|||
    |/       2/x\\ |            \2/||
    ||1 + tan |-||*|1 + -----------||
    |\        \2// |           2/x\||
    |              |    1 + tan |-|||
    \              \            \2///
-------------------------------------
                  2
atan⁡(tan⁡(x2)(1−tan⁡2(x2)tan⁡2(x2)+1+1)(tan⁡2(x2)+1))2\frac{\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)}}{2} 
    /                   /x\              \
    |              2*cot|-|              |
    |                   \2/              |
atan|------------------------------------|
    |              /      /        2/x\\\|
    |              |    2*|-1 + cot |-||||
    |/       2/x\\ |      \         \2//||
    ||1 + cot |-||*|2 + ----------------||
    |\        \2// |             2/x\   ||
    |              |      1 + cot |-|   ||
    \              \              \2/   //
------------------------------------------
                    2
atan⁡(2cot⁡(x2)(2(cot⁡2(x2)−1)cot⁡2(x2)+1+2)(cot⁡2(x2)+1))2\frac{\operatorname{atan}{\left(\frac{2 \cot{\left(\frac{x}{2} \right)}}{\left(\frac{2 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + 2\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)}}{2} 
    /           1            \
atan|------------------------|
    |/      2   \    /    pi\|
    ||2 + ------|*sec|x - --||
    \\    sec(x)/    \    2 //
------------------------------
              2
atan⁡(1(2+2sec⁡(x))sec⁡(x−π2))2\frac{\operatorname{atan}{\left(\frac{1}{\left(2 + \frac{2}{\sec{\left(x \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}} \right)}}{2} 
    /                /x\             \
    |             cot|-|             |
    |                \2/             |
atan|--------------------------------|
    |              /            2/x\\|
    |              |    -1 + cot |-|||
    |/       2/x\\ |             \2/||
    ||1 + cot |-||*|1 + ------------||
    |\        \2// |           2/x\ ||
    |              |    1 + cot |-| ||
    \              \            \2/ //
--------------------------------------
                  2
atan⁡(cot⁡(x2)(cot⁡2(x2)−1cot⁡2(x2)+1+1)(cot⁡2(x2)+1))2\frac{\operatorname{atan}{\left(\frac{\cot{\left(\frac{x}{2} \right)}}{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)}}{2} 
    /   /    pi\ \
    |cos|x - --| |
    |   \    2 / |
atan|------------|
    \2 + 2*cos(x)/
------------------
        2
atan⁡(cos⁡(x−π2)2cos⁡(x)+2)2\frac{\operatorname{atan}{\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{2 \cos{\left(x \right)} + 2} \right)}}{2} 
    /   sin(x)   \
atan|------------|
    \2 + 2*cos(x)/
------------------
        2
atan⁡(sin⁡(x)2cos⁡(x)+2)2\frac{\operatorname{atan}{\left(\frac{\sin{\left(x \right)}}{2 \cos{\left(x \right)} + 2} \right)}}{2} 
    /            1             \
atan|--------------------------|
    |  /      1   \    /    pi\|
    |2*|1 + ------|*sec|x - --||
    \  \    sec(x)/    \    2 //
--------------------------------
               2
atan⁡(12(1+1sec⁡(x))sec⁡(x−π2))2\frac{\operatorname{atan}{\left(\frac{1}{2 \left(1 + \frac{1}{\sec{\left(x \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}} \right)}}{2} 
    /       sin(x)      \
atan|-------------------|
    |  /       /    pi\\|
    |2*|1 + sin|x + --|||
    \  \       \    2 ///
-------------------------
            2
atan⁡(sin⁡(x)2(sin⁡(x+π2)+1))2\frac{\operatorname{atan}{\left(\frac{\sin{\left(x \right)}}{2 \left(\sin{\left(x + \frac{\pi}{2} \right)} + 1\right)} \right)}}{2} 
    /      sin(x)     \
atan|-----------------|
    |         /    pi\|
    |2 + 2*sin|x + --||
    \         \    2 //
-----------------------
           2
atan⁡(sin⁡(x)2sin⁡(x+π2)+2)2\frac{\operatorname{atan}{\left(\frac{\sin{\left(x \right)}}{2 \sin{\left(x + \frac{\pi}{2} \right)} + 2} \right)}}{2} 
    /                   /x\             \
    |              2*tan|-|             |
    |                   \2/             |
atan|-----------------------------------|
    |              /      /       2/x\\\|
    |              |    2*|1 - tan |-||||
    |/       2/x\\ |      \        \2//||
    ||1 + tan |-||*|2 + ---------------||
    |\        \2// |             2/x\  ||
    |              |      1 + tan |-|  ||
    \              \              \2/  //
-----------------------------------------
                    2
atan⁡(2tan⁡(x2)(2(1−tan⁡2(x2))tan⁡2(x2)+1+2)(tan⁡2(x2)+1))2\frac{\operatorname{atan}{\left(\frac{2 \tan{\left(\frac{x}{2} \right)}}{\left(\frac{2 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + 2\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)}}{2} 
    /    /    pi\  \
    | cos|x - --|  |
    |    \    2 /  |
atan|--------------|
    \2*(1 + cos(x))/
--------------------
         2
atan⁡(cos⁡(x−π2)2(cos⁡(x)+1))2\frac{\operatorname{atan}{\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{2 \left(\cos{\left(x \right)} + 1\right)} \right)}}{2} 
    /           1            \
atan|------------------------|
    |/         2     \       |
    ||2 + -----------|*csc(x)|
    ||       /pi    \|       |
    ||    csc|-- - x||       |
    \\       \2     //       /
------------------------------
              2
atan⁡(1(2+2csc⁡(−x+π2))csc⁡(x))2\frac{\operatorname{atan}{\left(\frac{1}{\left(2 + \frac{2}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc{\left(x \right)}} \right)}}{2} 
    /            1             \
atan|--------------------------|
    |  /         1     \       |
    |2*|1 + -----------|*csc(x)|
    |  |       /pi    \|       |
    |  |    csc|-- - x||       |
    \  \       \2     //       /
--------------------------------
               2
atan⁡(12(1+1csc⁡(−x+π2))csc⁡(x))2\frac{\operatorname{atan}{\left(\frac{1}{2 \left(1 + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc{\left(x \right)}} \right)}}{2} 
    /         1         \
atan|-------------------|
    |/      2   \       |
    ||2 + ------|*csc(x)|
    \\    sec(x)/       /
-------------------------
            2
atan⁡(1(2+2sec⁡(x))csc⁡(x))2\frac{\operatorname{atan}{\left(\frac{1}{\left(2 + \frac{2}{\sec{\left(x \right)}}\right) \csc{\left(x \right)}} \right)}}{2} 
atan(1/((2 + 2/sec(x))*csc(x)))/2
    © Sr Examen – Калькулятор